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Domination in Pythagorean fuzzy graphs

Granular Computing (2023)Cite this article

Abstract

Pythagorean fuzzy set theory is much more flexible to deal with obscure and uncertain knowledge comparative to fuzzy set theory. The principal aim of this article is to expand the meanings of domination and cobondage for Pythagorean fuzzy graphs by introducing the meanings of normal domination number, abnormal independent number, normal cobondage set, and normal cobondage number. Some relevant results of these meanings describe their significance as well as applicability. We present a decision-making problem in real-world applied example which discusses the agents affecting a corporation’s yield. The presented model is, in fact, an agent-based model wherein the impact score of each agent is divided into two types of direct and indirect influences.

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References

  • Akram M, Naz S (2019) A novel decision-making approach under complex Pythagorean fuzzy environment. Math Comput Appl 24(3):73

    MathSciNet  Google Scholar 

  • Akram M, Dar JM, Naz S (2019) Certain graphs under Pythagorean fuzzy environment. Complex Intell Syst 5(2):127–144

    Article  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets: theory and applications. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  • Banitalebi S, Ahn SS, Jun YB, Borzooei RA (2022) Normal m-domination and inverse m-domination in Pythagorean fuzzy graphs with application in decision making. J Intell Fuzzy Syst 43:5053–5062

    Article  Google Scholar 

  • Banitalebi S, Borzooei RA, Mohamadzadeh E (2021) 2-Domination in vague graphs. Algebr Struct Appl 8(2):203–222

    MATH  Google Scholar 

  • Chen SM, Ke JS, Chang JF (1990) Knowledge representation using fuzzy Petri nets. IEEE Trans Knowl Data Eng 2(3):311–319

    Article  Google Scholar 

  • Cockayne EJ, Hedetniemi ST (1977) Towards a theory of domination in graphs. Networks 7(3):247–261

    Article  MathSciNet  MATH  Google Scholar 

  • Gani AN, Chandrasekaran VT (2006) Domination in fuzzy graph. Adv Fuzzy Sets Syst 1(1):17–26

    MathSciNet  MATH  Google Scholar 

  • Gani AN, Devi KP (2015) 2-domination in fuzzy graphs. Int J Fuzzy Math Arch 9(1):119–124

    Google Scholar 

  • Gani AN, Devi KP, Pal M (2017) Reduction of domination parameter in fuzzy graphs. Glob J Pure Appl Math 13(7):3307–3315

    Google Scholar 

  • Kulli VR, Janakiram B (1996) The cobondage number of a graph. Discuss Math Graph Theory 16(2):111–117

    Article  MathSciNet  MATH  Google Scholar 

  • Naz S, Ashraf S, Akram M (2018) A novel approach to decision-making with Pythagorean fuzzy information. Mathematics 6:1–28

    Article  MATH  Google Scholar 

  • Parvathi R, Thamizhendhi G (2010) Domination in intuitionistic fuzzy graphs. Notes Intuit Fuzzy Sets 16(2):39–49

    MATH  Google Scholar 

  • Rosenfeld A (1975) Fuzzy graphs. In fuzzy sets and their applications to cognitive and decision processes (pp. 77-95). Academic press

  • Somasundaram A, Somasundaram S (1998) Domination in fuzzy graphs-I. Pattern Recognit Lett 19:787–791

    Article  MATH  Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (pp. 57-61). IEEE

  • Yager RR (2014) Pythagorean membership grades in multi-crteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Article  Google Scholar 

  • Zadeh LA (1999) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 100:9–34

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Cognitive Modeling and Simulation, Faculty of Artificial Intelligence and Cognitive Sciences, Imam Hossein University, Tehran, Iran

    Sadegh Banitalebi

  2. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    Rajab Ali Borzooei

Authors
  1. Sadegh Banitalebi
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  2. Rajab Ali Borzooei
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Correspondence to Rajab Ali Borzooei.

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Banitalebi, S., Borzooei, R.A. Domination in Pythagorean fuzzy graphs. Granul. Comput. (2023). https://doi.org/10.1007/s41066-023-00362-5

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  • DOI: https://doi.org/10.1007/s41066-023-00362-5

Keywords

  • Abnormal independent number
  • Normal cobondage set
  • Normal cobondage number
  • Normal domination number
  • Pythagorean fuzzy graph